The carrier frequency generated by a tank circuit containing 1 nF capacitor and 10 μH inductor i

step 1 Carrier frequency generated by the tank circuit containing 1 nanofarad capacitor. Thus, the capa

The carrier frequency generated by a tank circuit containing...

The carrier frequency generated by a tank circuit containing $1 \mathrm{nF}$ capacitor and $10 \mu \mathrm{H}$ inductor is
(a) $1592 \mathrm{~Hz}$
(b) $1592 \mathrm{MHz}$
(c) $1592 \mathrm{kHz}$
(d) $159.2 \mathrm{~Hz}$

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Key Concepts

Unit Conversion

Accurate unit conversion is crucial in calculations involving electrical circuits. Converting values of capacitance and inductance to the standard SI units (farads for capacitance and henries for inductance) ensures that the resonant frequency is correctly computed using the resonant frequency formula, avoiding any errors related to scaling factors.

LC Circuit

An LC circuit, often referred to as a tank circuit, is a fundamental arrangement in electronics that consists of an inductor (L) and a capacitor (C) connected together. It is capable of generating oscillations or resonating at a specific frequency where energy continuously transfers between the magnetic field of the inductor and the electric field of the capacitor.

Resonant Frequency Formula

The resonant frequency of an LC circuit is determined by the formula f = 1/(2??(LC)). This formula shows that the frequency of oscillation is inversely proportional to the square root of the product of the inductance and the capacitance, highlighting the dependency of the oscillatory behavior on the physical components of the circuit.

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